"pose, but at any point, you can move it only by a forward motion and a steering angle. So it has two control DOFs and three representational DOFs; i.e. it is non-holonomic. A fixed-wing aircraft, with 3–4 control DOFs (forward motion, roll, pitch, and to a limited extent, yaw) in a 3-D space, is also non-holonomic, as it cannot move directly up/down or left/right. A summary of formulas and methods for computing the degrees-of-freedom in mechanical systems has been given by Pennestri, Cavacece, and Vita. In electrical engineering ""degrees of freedom"" is often used to describe the number of directions"
"Degree (angle) A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of angular measure is the radian, but it is mentioned in the SI brochure as an accepted unit. Because a full rotation equals 2 radians, one degree is equivalent to radians. The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is"
"geometry is that the sum of the interior angles of a triangle is greater than 180 degrees. In the spherical model, for example, a triangle can be constructed with vertices at the locations where the three positive Cartesian coordinate axes intersect the sphere, and all three of its internal angles are 90 degrees, summing to 270 degrees. For sufficiently small triangles, the excess over 180 degrees can be made arbitrarily small. The Pythagorean theorem fails in elliptic geometry. In the 90°–90°–90° triangle described above, all three sides have the same length, and consequently do not satisfy formula_1. The Pythagorean result"
"Angle of rotation In mathematics, the angle of rotation is a measurement of the amount, namely the angle, that a figure is rotated about a fixed point, often the center of a circle. A clockwise rotation is considered a negative rotation, so that, for instance, a rotation of 310° (counterclockwise) can also be called a rotation of –50° (since , a full rotation (turn)). A counterclockwise rotation of more than one complete turn is normally measured modulo 360°, meaning that 360° is subtracted off as many times as possible to leave a non-negative measurement less than 360°. For example, the"
"an angle of 40° (1/9 of the 360° ecliptic). An orb of 40±1° is allowed. It indicates an energy of perfection and/or idealization. The ""parallel"" and ""antiparallel"" (or ""contraparallel"") are two other aspects which refer to degrees of declination above or below the celestial equator. They are considered moderate influences, though not much research has gone into studying these particular aspects. Astrological aspect In astrology, an aspect is an angle the planets make to each other in the horoscope, also to the ascendant, midheaven, descendant, lower midheaven, and other points of astrological interest. Aspects are measured by the angular distance"
"this system. In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more ""natural"" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number 360. One complete turn (360°) is equal to 2"""" radians, so 180° is equal to radians, or equivalently, the degree is a mathematical constant: 1° = . The turn (or revolution, full circle, full rotation, cycle) is used in technology and science. One turn is equal to 360°."
"Right angle In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin ""angulus rectus""; here ""rectus"" means ""upright"", referring to the vertical perpendicular to a horizontal base line. Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied"
"angle formula_13 is greater than 90° and less than 180°, we can deduce from the conditional (if-then) statement that formula_13 is an obtuse angle. However, if we are given that formula_13 is an obtuse angle, we cannot deduce from the conditional statement that 90° < formula_13 < 180°. It might be true that other angles outside this range are also obtuse. Modus tollens (also known as ""the law of contrapositive"") is a deductive rule of inference. It validates an argument that has as premises a conditional statement (formula_1) and the negation of the consequent (formula_22) and as conclusion the negation"
"Likewise, the angle between meridian and parallel might have changed from 90° to some other value. Indeed, unless the map is conformal, all angles except the one subtended by the semi-major axis and semi-minor axis of the ellipse might have changed. A particular angle will have changed the most, and value of that maximum change is known as the angular deformation, denoted as ""θ′"". Generally which angle that is and how it is oriented do not figure prominently in distortion analysis. It is the value of the change that is significant. The values of ""h"", ""k"", and ""θ′"" can be"
"Gradian The gradian is a unit of measurement of an angle, equivalent to formula_1 of a turn, formula_2 of a degree, or formula_3 of a radian. The gradian is defined as formula_4 of the right angle (in other words, there are 100 gradians in the right angle), which implies a full turn being 400 gradians. It is also known as gon (from Greek /""gōnía"" for angle), grad, or grade. In continental Europe, the French term ""centigrade"" was in use for one hundredth of a grad. This was one reason for the adoption of the term Celsius to replace centigrade as"
"above should be treated as rough rule of thumb approximations only. Not all angle measurements are angular units, for an angular measurement it is definitional that the angle addition postulate holds. Some angle measurements where the angle addition postulate does not holds. Angular unit Throughout history, angles have been measured in many different units. The most contemporary units are the degree ( ° ) and radian (rad), but many others have been used throughout history. The purpose of this page is to aggregate other concepts pertaining to the angular unit, where additional explanation can be provided. The size of a"
"90 (number) 90 (ninety) is the natural number preceded by 89 and followed by 91. In the English language, the numbers 90 and 19 are often confused, as sounding very similar. When carefully enunciated, they differ in which syllable is stressed: 19 /naɪnˈtiːn/ vs 90 /ˈnaɪnti/. However, in dates such as 1999, and when contrasting numbers in the teens and when counting, such as 17, 18, 19, the stress shifts to the first syllable: 19 /ˈnaɪntiːn/. 90 is: In normal space, the interior angles of a rectangle measure 90 degrees each. Also, in a right triangle, the angle opposing the"
"the angle is measured as long as each angle is measured in the same unit. One ""radian"" is the angle subtended by an arc of a circle that has the same length as the circle's radius. The radian is the derived quantity of angular measurement in the SI system. By definition, it is dimensionless, though it may be specified as ""rad"" to avoid ambiguity. Angles measured in degrees, are shown with the symbol °. Subdivisions of the degree are minute (symbol ', 1' = 1/60°) and second {symbol "", 1"" = 1/3600°}. An angle of 360° corresponds to the angle"
"Right triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the ""hypotenuse"" (side ""c"" in the figure). The sides adjacent to the right angle are called ""legs"" (or ""catheti"", singular: ""cathetus""). Side ""a"" may be identified as the side ""adjacent to angle B"" and ""opposed to"" (or ""opposite"") ""angle A"", while side ""b"" is the side ""adjacent to"
"Right triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the ""hypotenuse"" (side ""c"" in the figure). The sides adjacent to the right angle are called ""legs"" (or ""catheti"", singular: ""cathetus""). Side ""a"" may be identified as the side ""adjacent to angle B"" and ""opposed to"" (or ""opposite"") ""angle A"", while side ""b"" is the side ""adjacent to"
"with an inclination between 0 and 90 degrees is orbiting or revolving in the same direction as the primary is rotating. An object with an inclination of exactly 90 degrees has a perpendicular orbit that is neither prograde nor retrograde. An object with an inclination between 90 degrees and 180 degrees is in a retrograde orbit. A celestial object's axial tilt indicates whether the object's ""rotation"" is prograde or retrograde. Axial tilt is the angle between an object's rotation axis and a line perpendicular to its orbital plane passing through the object's centre. An object with an axial tilt up"
"65° 39′ 18″ West 85.69 feet"" would describe a line running from the starting point 85.69 feet in a direction 65° 39′ 18″ (or 65.655°) away from north toward the west. The arcminute is commonly found in the firearms industry and literature, particularly concerning the accuracy of rifles, though the industry refers to it as minute of angle (MOA). It is especially popular with shooters familiar with the imperial measurement system because 1 MOA is subtended by a sphere with a diameter of 1.047 inches at 100 yards (2.908 cm at 100 m), a traditional distance on U.S. target ranges."
"A pitch angle of 90 degrees is a particle that is locally mirroring (see: Magnetosphere particle motion). The equatorial pitch angle of a particle is the pitch angle of the particle at the Earth's geomagnetic equator. This angle defines the loss cone of a particle. The loss cone is the set of angles where the particle will strike the atmosphere and no longer be trapped in the magnetosphere while particles with pitch angles outside the loss cone will continue to be trapped. The loss cone is defined as the probability of particle loss from the magnetic bottle which is: Where"
"Angular unit Throughout history, angles have been measured in many different units. The most contemporary units are the degree ( ° ) and radian (rad), but many others have been used throughout history. The purpose of this page is to aggregate other concepts pertaining to the angular unit, where additional explanation can be provided. The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are said to be ""equal"" or ""congruent"" or ""equal in measure"". In some contexts, such"
"geometry, it is the number of seconds in a minute, and the number of minutes in a degree. In normal space, the three interior angles of an equilateral triangle each measure 60 degrees, adding up to 180 degrees. Because it is divisible by the sum of its digits in base 10, it is a Harshad number. A number system with base 60 is called sexagesimal (the original meaning of ""sexagesimal"" is sixtieth). It is the smallest positive integer that is written with only the smallest and the largest digit of base 2 (binary), base 3 (ternary) and base 4 (quaternary)."
"Acute and obtuse triangles An acute triangle is a triangle with all three angles acute (less than 90°). An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180°, no triangle can have more than one obtuse angle. Acute and obtuse triangles are the two different types of oblique triangles—triangles that are not right triangles because they have no 90° angle. In all triangles, the centroid—the intersection of the medians, each of which connects a vertex with the midpoint of the opposite side—and the incenter—the center of"
"Rake (angle) A rake is an angle of slope measured from horizontal, or from a vertical line 90° perpendicular to horizontal. A 60° rake would mean that the line is pointing 60 up from horizontal, either forwards or backwards relative to the object. There are many ways in which the term can be used. The rake of a ships prow measures the angle at which the prow rises from the water (the rake below water being called the bow rake). A motorcycle or bicycle fork rake measures the angle at which the forks are angled down towards the ground. In"
"Solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The point from which the object is viewed is called the ""apex"" of the solid angle, and the object is said to ""subtend"" its solid angle from that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a ""steradian"" (symbol: sr). One steradian"
"be less than 90 degrees. For example, if Point B is located exactly southeast of Point A, the bearing from Point A to Point B is S 45° E. The US Army defines the ""azimuth"" between Point A and Point B as the angle, measured in the clockwise direction, between the north reference ray and Ray AB. For example, if the bearing between Point A and Point B is S 45° E, the azimuth between Point A and Point B is 135°. The angle value in a bearing can be specified in the units of degrees, mils, or grad. An"
"""AOC"", then The measure of the angle ""AOC"" is the sum of the measure of angle AOB and the measure of angle ""BOC"". In this postulate it does not matter in which unit the angle is measured as long as each angle is measured in the same unit. Units used to represent angles are listed below in descending magnitude order. Of these units, the ""degree"" and the ""radian"" are by far the most commonly used. Angles expressed in radians are dimensionless for the purposes of dimensional analysis. Most units of angular measurement are defined such that one ""turn"" (i.e. one"
"Turn (geometry) A turn is a unit of plane angle measurement equal to 2 radians, 360 degrees or 400 gradians. A turn is also referred to as a cycle (abbreviated cyc), revolution (abbreviated rev), complete rotation (abbreviated rot) or full circle. Subdivisions of a turn include half turns, quarter turns, centiturns, milliturns, points, etc. A turn can be divided in 100 centiturns or milliturns, with each milliturn corresponding to an angle of 0.36°, which can also be written as 21′ 36″. A protractor divided in centiturns is normally called a percentage protractor. Binary fractions of a turn are also used."
"made of wood or metal (usually brass) divided on its arc side into 90 equal parts or degrees. The 90 divisions are gathered in 18 groups of five degrees each and are generally numbered both ways from the ends of the arc. That is, one set of numbers begins at the left end of the arc and goes to 90 at the right end while the other set the zero is at the right and the 90 is at the left. This double numbering enables the instrument to measure either celestial altitude or zenith distance or both simultaneously. At the"
"distinguished by left-handed fittings. In trigonometry and mathematics in general, plane angles are conventionally measured counterclockwise, starting with 0° or 0 radians pointing directly to the right (or east), and 90° pointing straight up (or north). However, in navigation, compass headings increase clockwise around the compass face, starting with 0° at the top of the compass (the northerly direction), with 90° to the right (east). A circle defined parametrically in a positive Cartesian plane by the equations and is traced counterclockwise as the angle ""t"" increases in value, from the right-most point at . An alternative formulation with sin and"
"Orb (astrology) In astrology, the orb is how much an angle made by two points differs from the exactness of an aspect. A trine, for instance, is 120 degrees. If two points were 123 degrees apart, they would be said to be in a trine with an orb of 3 degrees. It is generally held in astrological delineation that the larger the orb, the less powerful the aspect's effect is. For example, if the sun is located in the sign Aquarius at 15 degrees and the moon is also going through Aquarius, then the moon's orb of influence will begin"
"an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles. The ""exterior"" or ""external bisector"" is the line that divides the supplementary angle (of 180° minus the original angle), formed by one side forming the original angle and the extension of the other side, into two equal angles. To bisect an angle with straightedge and compass, one draws a circle whose center is the vertex. The circle meets the angle at two points: one on each leg. Using each of these points as a center, draw two circles of"
". It is approximately equal to one milliradian ( ). A mil measuring of a revolution originated in the imperial Russian army, where an equilateral chord was divided into tenths to give a circle of 600 units. This may be seen on a lining plane (an early device for aiming indirect fire artillery) dating from about 1900 in the St. Petersburg Museum of Artillery. Degree (angle) A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360"
"Declination In astronomy, declination (abbreviated dec; symbol δ) is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declination's angle is measured north or south of the celestial equator, along the hour circle passing through the point in question. The root of the word ""declination"" (Latin, ""declinatio"") means ""a bending away"" or ""a bending down"". It comes from the same root as the words ""incline"" (""bend toward"") and ""recline"" (""bend backward""). In some 18th and 19th century astronomical texts, declination is given as ""North Pole Distance"""
"consists of a beam, a graduated dial and a blade which is connected to a swivel plate (with Vernier scale) by thumb nut and clamp. When the edges of the beam and blade are parallel, a small mark on the swivel plate coincides with the zero line on the graduated dial. To measure an angle between the beam and the blade of 90° or less, the reading may be obtained direct from the graduation number on the dial indicated by the mark on the swivel plate. To measure an angle of over 90°, subtract the number of degrees as indicated"